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Computer Simulation of LiquidsSecond Edition$
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Michael P. Allen and Dominic J. Tildesley

Print publication date: 2017

Print ISBN-13: 9780198803195

Published to Oxford Scholarship Online: November 2017

DOI: 10.1093/oso/9780198803195.001.0001

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Monte Carlo methods

Monte Carlo methods

(p.147) 4 Monte Carlo methods
Computer Simulation of Liquids

Michael P. Allen

Dominic J. Tildesley

Oxford University Press

The estimation of integrals by Monte Carlo sampling is introduced through a simple example. The chapter then explains importance sampling, and the use of the Metropolis and Barker forms of the transition matrix defined in terms of the underlying matrix of the Markov chain. The creation of an appropriately weighted set of states in the canonical ensemble is described in detail and the method is extended to the isothermal–isobaric, grand canonical and semi-grand ensembles. The Monte Carlo simulation of molecular fluids and fluids containing flexible molecules using a reptation algorithm is discussed. The parallel tempering or replica exchange method for more efficient exploration of the phase space is introduced, and recent advances including solute tempering and convective replica exchange algorithms are described.

Keywords:   Importance-sampling, Markov-chain, parallel-tempering, replica-exchange, constant-temperature, constant-pressure, grand-canonical, convective-replica-exchange, reptation

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